Local well-posedness and blow-up of solution for a higher-order wave equation with viscoelastic term and variable-exponent
سال انتشار: 1402
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 79
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شناسه ملی سند علمی:
JR_IJNAA-14-4_010
تاریخ نمایه سازی: 5 شهریور 1402
چکیده مقاله:
We investigate in this paper a value problem related to the following nonlinear higher-order wave equation \eta_{tt}+\left( -\Delta\right) ^{m}\eta-% %TCIMACRO{\dint \limits_{۰}^{t}}% %BeginExpansion {\displaystyle\int\limits_{۰}^{t}} %EndExpansion g\left( t-s\right) \left( -\Delta\right) ^{m}\eta\left( s\right) ds+\eta_{t}=\left\vert \eta\right\vert ^{p\left( x\right) -۲}\eta. Firstly, we prove the existence and uniqueness of the local solution under suitable conditions for the relaxation function g and viable-exponent p\left( .\right) , using a method, which is a mixture of the Faedo-Galarkin and Banach fixed point theorem, and prove also the solution blows up in finite time. Finally, we give a two-dimensional numerical example to illustrate the blow-up result.
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نویسندگان
Boughamsa Wissem
Department of Mathematics, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of ۲۰ August ۱۹۵۵, Skikda, Algeria
Ouaoua Amar
Department of Sciences and Technology, Laboratory of Applied Mathematics and History and Didactics of Mathematics (LAMAHIS), University of ۲۰ August ۱۹۵۵, Skikda, Algeria